Properties

Label 29.18.a.b.1.2
Level $29$
Weight $18$
Character 29.1
Self dual yes
Analytic conductor $53.134$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(53.1344053299\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q-687.348 q^{2} -21372.9 q^{3} +341375. q^{4} -1.16997e6 q^{5} +1.46906e7 q^{6} -9.37855e6 q^{7} -1.44551e8 q^{8} +3.27660e8 q^{9} +O(q^{10})\) \(q-687.348 q^{2} -21372.9 q^{3} +341375. q^{4} -1.16997e6 q^{5} +1.46906e7 q^{6} -9.37855e6 q^{7} -1.44551e8 q^{8} +3.27660e8 q^{9} +8.04176e8 q^{10} +8.41895e8 q^{11} -7.29616e9 q^{12} +4.06492e9 q^{13} +6.44633e9 q^{14} +2.50056e10 q^{15} +5.46121e10 q^{16} +1.44158e10 q^{17} -2.25216e11 q^{18} -2.26386e9 q^{19} -3.99398e11 q^{20} +2.00447e11 q^{21} -5.78675e11 q^{22} -2.37009e11 q^{23} +3.08947e12 q^{24} +6.05889e11 q^{25} -2.79401e12 q^{26} -4.24295e12 q^{27} -3.20160e12 q^{28} +5.00246e11 q^{29} -1.71876e13 q^{30} +7.30920e12 q^{31} -1.85909e13 q^{32} -1.79937e13 q^{33} -9.90864e12 q^{34} +1.09726e13 q^{35} +1.11855e14 q^{36} +1.73834e12 q^{37} +1.55606e12 q^{38} -8.68790e13 q^{39} +1.69120e14 q^{40} -2.43176e13 q^{41} -1.37777e14 q^{42} +8.01944e13 q^{43} +2.87402e14 q^{44} -3.83352e14 q^{45} +1.62907e14 q^{46} +9.47943e13 q^{47} -1.16722e15 q^{48} -1.44673e14 q^{49} -4.16456e14 q^{50} -3.08107e14 q^{51} +1.38766e15 q^{52} -5.06029e14 q^{53} +2.91638e15 q^{54} -9.84992e14 q^{55} +1.35568e15 q^{56} +4.83852e13 q^{57} -3.43843e14 q^{58} +1.89499e15 q^{59} +8.53629e15 q^{60} +5.95411e14 q^{61} -5.02396e15 q^{62} -3.07298e15 q^{63} +5.62029e15 q^{64} -4.75583e15 q^{65} +1.23679e16 q^{66} +7.78620e14 q^{67} +4.92118e15 q^{68} +5.06556e15 q^{69} -7.54200e15 q^{70} -2.17222e15 q^{71} -4.73636e16 q^{72} +1.29421e16 q^{73} -1.19485e15 q^{74} -1.29496e16 q^{75} -7.72824e14 q^{76} -7.89576e15 q^{77} +5.97161e16 q^{78} +1.99974e16 q^{79} -6.38945e16 q^{80} +4.83700e16 q^{81} +1.67147e16 q^{82} -2.62251e16 q^{83} +6.84274e16 q^{84} -1.68660e16 q^{85} -5.51214e16 q^{86} -1.06917e16 q^{87} -1.21697e17 q^{88} -3.29297e15 q^{89} +2.63496e17 q^{90} -3.81230e16 q^{91} -8.09087e16 q^{92} -1.56219e17 q^{93} -6.51566e16 q^{94} +2.64865e15 q^{95} +3.97341e17 q^{96} -5.04465e16 q^{97} +9.94408e16 q^{98} +2.75856e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} + O(q^{10}) \) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} - 224469478q^{10} + 1203139534q^{11} - 5164251122q^{12} + 3854339312q^{13} + 25262272904q^{14} + 28324474306q^{15} + 196520815922q^{16} + 76444714794q^{17} + 75758949126q^{18} + 246497292428q^{19} - 46900976670q^{20} + 360937126704q^{21} - 275001533522q^{22} + 213498528140q^{23} - 451123453870q^{24} + 3898884886997q^{25} - 3609347694206q^{26} - 2718903745978q^{27} - 5946174617200q^{28} + 10505174672181q^{29} - 20237658929454q^{30} + 16670029895798q^{31} - 42141001912046q^{32} - 7157109761394q^{33} + 12785761151136q^{34} + 46677934312888q^{35} + 132137824374868q^{36} + 53445659988410q^{37} + 76581637956388q^{38} + 79233849032530q^{39} + 193617444734146q^{40} - 20814769309298q^{41} + 76690667258352q^{42} + 185498647364454q^{43} + 315429066899678q^{44} - 486270821438526q^{45} + 261474367677132q^{46} + 389503471719450q^{47} - 101509672247630q^{48} + 730079062141437q^{49} + 1482269666368354q^{50} + 718238208473988q^{51} + 1966802817157170q^{52} + 747441265526156q^{53} + 5692893333117030q^{54} + 1639109418219546q^{55} + 5657219329125240q^{56} + 4694352396864932q^{57} + 128063081718016q^{58} + 5280258638332960q^{59} + 15251367906033378q^{60} + 5813675353074254q^{61} + 6242066590947250q^{62} + 10947760075450368q^{63} + 24583792057508902q^{64} + 19190799243789974q^{65} + 41877805444482390q^{66} + 13420580230958268q^{67} + 24771837384165388q^{68} + 30973047049935252q^{69} + 8505088080182440q^{70} + 4824462822979508q^{71} + 1180071997284592q^{72} + 11228916281304662q^{73} - 89132715356772q^{74} + 59161419576630296q^{75} + 57466858643173460q^{76} + 58741564492720064q^{77} + 142050530910210210q^{78} + 71718598015696758q^{79} + 48350023652407550q^{80} + 75805931446703569q^{81} + 188661890754420812q^{82} + 50769377111735608q^{83} + 198832046985593048q^{84} + 53422044849490784q^{85} + 35014892323844118q^{86} + 11988905533023326q^{87} + 37459283979085258q^{88} - 70981414576978018q^{89} + 57211029866143724q^{90} + 112933943315157320q^{91} - 103019729095759724q^{92} - 350358290646906646q^{93} - 150286322409612578q^{94} - 102561321856584476q^{95} - 213770098354021866q^{96} - 130930167251505210q^{97} - 537387515497557296q^{98} - 95267700931431064q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −687.348 −1.89855 −0.949274 0.314451i \(-0.898179\pi\)
−0.949274 + 0.314451i \(0.898179\pi\)
\(3\) −21372.9 −1.88076 −0.940378 0.340130i \(-0.889529\pi\)
−0.940378 + 0.340130i \(0.889529\pi\)
\(4\) 341375. 2.60448
\(5\) −1.16997e6 −1.33946 −0.669730 0.742605i \(-0.733590\pi\)
−0.669730 + 0.742605i \(0.733590\pi\)
\(6\) 1.46906e7 3.57071
\(7\) −9.37855e6 −0.614897 −0.307449 0.951565i \(-0.599475\pi\)
−0.307449 + 0.951565i \(0.599475\pi\)
\(8\) −1.44551e8 −3.04618
\(9\) 3.27660e8 2.53725
\(10\) 8.04176e8 2.54303
\(11\) 8.41895e8 1.18419 0.592093 0.805869i \(-0.298302\pi\)
0.592093 + 0.805869i \(0.298302\pi\)
\(12\) −7.29616e9 −4.89840
\(13\) 4.06492e9 1.38208 0.691040 0.722817i \(-0.257153\pi\)
0.691040 + 0.722817i \(0.257153\pi\)
\(14\) 6.44633e9 1.16741
\(15\) 2.50056e10 2.51920
\(16\) 5.46121e10 3.17884
\(17\) 1.44158e10 0.501212 0.250606 0.968089i \(-0.419370\pi\)
0.250606 + 0.968089i \(0.419370\pi\)
\(18\) −2.25216e11 −4.81708
\(19\) −2.26386e9 −0.0305804 −0.0152902 0.999883i \(-0.504867\pi\)
−0.0152902 + 0.999883i \(0.504867\pi\)
\(20\) −3.99398e11 −3.48860
\(21\) 2.00447e11 1.15647
\(22\) −5.78675e11 −2.24823
\(23\) −2.37009e11 −0.631070 −0.315535 0.948914i \(-0.602184\pi\)
−0.315535 + 0.948914i \(0.602184\pi\)
\(24\) 3.08947e12 5.72913
\(25\) 6.05889e11 0.794151
\(26\) −2.79401e12 −2.62394
\(27\) −4.24295e12 −2.89118
\(28\) −3.20160e12 −1.60149
\(29\) 5.00246e11 0.185695
\(30\) −1.71876e13 −4.78281
\(31\) 7.30920e12 1.53920 0.769601 0.638526i \(-0.220455\pi\)
0.769601 + 0.638526i \(0.220455\pi\)
\(32\) −1.85909e13 −2.98900
\(33\) −1.79937e13 −2.22717
\(34\) −9.90864e12 −0.951576
\(35\) 1.09726e13 0.823630
\(36\) 1.11855e14 6.60821
\(37\) 1.73834e12 0.0813619 0.0406810 0.999172i \(-0.487047\pi\)
0.0406810 + 0.999172i \(0.487047\pi\)
\(38\) 1.55606e12 0.0580584
\(39\) −8.68790e13 −2.59935
\(40\) 1.69120e14 4.08024
\(41\) −2.43176e13 −0.475618 −0.237809 0.971312i \(-0.576429\pi\)
−0.237809 + 0.971312i \(0.576429\pi\)
\(42\) −1.37777e14 −2.19562
\(43\) 8.01944e13 1.04631 0.523157 0.852236i \(-0.324754\pi\)
0.523157 + 0.852236i \(0.324754\pi\)
\(44\) 2.87402e14 3.08419
\(45\) −3.83352e14 −3.39854
\(46\) 1.62907e14 1.19812
\(47\) 9.47943e13 0.580698 0.290349 0.956921i \(-0.406229\pi\)
0.290349 + 0.956921i \(0.406229\pi\)
\(48\) −1.16722e15 −5.97863
\(49\) −1.44673e14 −0.621901
\(50\) −4.16456e14 −1.50773
\(51\) −3.08107e14 −0.942659
\(52\) 1.38766e15 3.59960
\(53\) −5.06029e14 −1.11643 −0.558214 0.829697i \(-0.688513\pi\)
−0.558214 + 0.829697i \(0.688513\pi\)
\(54\) 2.91638e15 5.48905
\(55\) −9.84992e14 −1.58617
\(56\) 1.35568e15 1.87309
\(57\) 4.83852e13 0.0575144
\(58\) −3.43843e14 −0.352551
\(59\) 1.89499e15 1.68022 0.840108 0.542419i \(-0.182491\pi\)
0.840108 + 0.542419i \(0.182491\pi\)
\(60\) 8.53629e15 6.56120
\(61\) 5.95411e14 0.397661 0.198831 0.980034i \(-0.436286\pi\)
0.198831 + 0.980034i \(0.436286\pi\)
\(62\) −5.02396e15 −2.92225
\(63\) −3.07298e15 −1.56014
\(64\) 5.62029e15 2.49591
\(65\) −4.75583e15 −1.85124
\(66\) 1.23679e16 4.22838
\(67\) 7.78620e14 0.234256 0.117128 0.993117i \(-0.462631\pi\)
0.117128 + 0.993117i \(0.462631\pi\)
\(68\) 4.92118e15 1.30540
\(69\) 5.06556e15 1.18689
\(70\) −7.54200e15 −1.56370
\(71\) −2.17222e15 −0.399215 −0.199608 0.979876i \(-0.563967\pi\)
−0.199608 + 0.979876i \(0.563967\pi\)
\(72\) −4.73636e16 −7.72891
\(73\) 1.29421e16 1.87829 0.939143 0.343527i \(-0.111622\pi\)
0.939143 + 0.343527i \(0.111622\pi\)
\(74\) −1.19485e15 −0.154469
\(75\) −1.29496e16 −1.49360
\(76\) −7.72824e14 −0.0796462
\(77\) −7.89576e15 −0.728153
\(78\) 5.97161e16 4.93500
\(79\) 1.99974e16 1.48301 0.741504 0.670948i \(-0.234113\pi\)
0.741504 + 0.670948i \(0.234113\pi\)
\(80\) −6.38945e16 −4.25793
\(81\) 4.83700e16 2.90037
\(82\) 1.67147e16 0.902983
\(83\) −2.62251e16 −1.27807 −0.639034 0.769178i \(-0.720666\pi\)
−0.639034 + 0.769178i \(0.720666\pi\)
\(84\) 6.84274e16 3.01201
\(85\) −1.68660e16 −0.671354
\(86\) −5.51214e16 −1.98648
\(87\) −1.06917e16 −0.349248
\(88\) −1.21697e17 −3.60725
\(89\) −3.29297e15 −0.0886693 −0.0443347 0.999017i \(-0.514117\pi\)
−0.0443347 + 0.999017i \(0.514117\pi\)
\(90\) 2.63496e17 6.45228
\(91\) −3.81230e16 −0.849837
\(92\) −8.09087e16 −1.64361
\(93\) −1.56219e17 −2.89486
\(94\) −6.51566e16 −1.10248
\(95\) 2.64865e15 0.0409612
\(96\) 3.97341e17 5.62158
\(97\) −5.04465e16 −0.653539 −0.326769 0.945104i \(-0.605960\pi\)
−0.326769 + 0.945104i \(0.605960\pi\)
\(98\) 9.94408e16 1.18071
\(99\) 2.75856e17 3.00457
\(100\) 2.06835e17 2.06835
\(101\) −8.81990e16 −0.810460 −0.405230 0.914215i \(-0.632809\pi\)
−0.405230 + 0.914215i \(0.632809\pi\)
\(102\) 2.11776e17 1.78968
\(103\) −1.15173e16 −0.0895848 −0.0447924 0.998996i \(-0.514263\pi\)
−0.0447924 + 0.998996i \(0.514263\pi\)
\(104\) −5.87587e17 −4.21007
\(105\) −2.34517e17 −1.54905
\(106\) 3.47818e17 2.11959
\(107\) 9.87881e16 0.555831 0.277915 0.960606i \(-0.410357\pi\)
0.277915 + 0.960606i \(0.410357\pi\)
\(108\) −1.44843e18 −7.53003
\(109\) −2.17356e17 −1.04483 −0.522417 0.852690i \(-0.674969\pi\)
−0.522417 + 0.852690i \(0.674969\pi\)
\(110\) 6.77032e17 3.01142
\(111\) −3.71535e16 −0.153022
\(112\) −5.12182e17 −1.95466
\(113\) 6.64718e16 0.235218 0.117609 0.993060i \(-0.462477\pi\)
0.117609 + 0.993060i \(0.462477\pi\)
\(114\) −3.32574e16 −0.109194
\(115\) 2.77293e17 0.845292
\(116\) 1.70771e17 0.483640
\(117\) 1.33191e18 3.50667
\(118\) −1.30252e18 −3.18997
\(119\) −1.35199e17 −0.308194
\(120\) −3.61459e18 −7.67394
\(121\) 2.03341e17 0.402298
\(122\) −4.09254e17 −0.754978
\(123\) 5.19738e17 0.894522
\(124\) 2.49517e18 4.00882
\(125\) 1.83744e17 0.275726
\(126\) 2.11220e18 2.96201
\(127\) 1.32550e17 0.173799 0.0868997 0.996217i \(-0.472304\pi\)
0.0868997 + 0.996217i \(0.472304\pi\)
\(128\) −1.42635e18 −1.74961
\(129\) −1.71399e18 −1.96786
\(130\) 3.26891e18 3.51466
\(131\) −1.73136e18 −1.74414 −0.872071 0.489380i \(-0.837223\pi\)
−0.872071 + 0.489380i \(0.837223\pi\)
\(132\) −6.14260e18 −5.80062
\(133\) 2.12317e16 0.0188038
\(134\) −5.35183e17 −0.444745
\(135\) 4.96412e18 3.87262
\(136\) −2.08381e18 −1.52679
\(137\) 2.19249e17 0.150943 0.0754713 0.997148i \(-0.475954\pi\)
0.0754713 + 0.997148i \(0.475954\pi\)
\(138\) −3.48180e18 −2.25336
\(139\) 2.34745e18 1.42879 0.714397 0.699740i \(-0.246701\pi\)
0.714397 + 0.699740i \(0.246701\pi\)
\(140\) 3.74577e18 2.14513
\(141\) −2.02603e18 −1.09215
\(142\) 1.49307e18 0.757929
\(143\) 3.42223e18 1.63664
\(144\) 1.78942e19 8.06550
\(145\) −5.85273e17 −0.248731
\(146\) −8.89574e18 −3.56601
\(147\) 3.09209e18 1.16965
\(148\) 5.93427e17 0.211906
\(149\) 1.95450e18 0.659100 0.329550 0.944138i \(-0.393103\pi\)
0.329550 + 0.944138i \(0.393103\pi\)
\(150\) 8.90088e18 2.83568
\(151\) 1.84272e18 0.554824 0.277412 0.960751i \(-0.410523\pi\)
0.277412 + 0.960751i \(0.410523\pi\)
\(152\) 3.27243e17 0.0931536
\(153\) 4.72347e18 1.27170
\(154\) 5.42713e18 1.38243
\(155\) −8.55154e18 −2.06170
\(156\) −2.96583e19 −6.76997
\(157\) −3.13944e17 −0.0678743 −0.0339372 0.999424i \(-0.510805\pi\)
−0.0339372 + 0.999424i \(0.510805\pi\)
\(158\) −1.37452e19 −2.81556
\(159\) 1.08153e19 2.09973
\(160\) 2.17508e19 4.00364
\(161\) 2.22280e18 0.388043
\(162\) −3.32470e19 −5.50648
\(163\) −2.83376e18 −0.445419 −0.222710 0.974885i \(-0.571490\pi\)
−0.222710 + 0.974885i \(0.571490\pi\)
\(164\) −8.30142e18 −1.23874
\(165\) 2.10521e19 2.98320
\(166\) 1.80258e19 2.42647
\(167\) −8.86986e18 −1.13456 −0.567279 0.823526i \(-0.692004\pi\)
−0.567279 + 0.823526i \(0.692004\pi\)
\(168\) −2.89748e19 −3.52283
\(169\) 7.87312e18 0.910144
\(170\) 1.15928e19 1.27460
\(171\) −7.41776e17 −0.0775901
\(172\) 2.73763e19 2.72510
\(173\) 9.67216e18 0.916498 0.458249 0.888824i \(-0.348477\pi\)
0.458249 + 0.888824i \(0.348477\pi\)
\(174\) 7.34892e18 0.663063
\(175\) −5.68236e18 −0.488321
\(176\) 4.59777e19 3.76434
\(177\) −4.05014e19 −3.16008
\(178\) 2.26342e18 0.168343
\(179\) −2.55136e19 −1.80934 −0.904670 0.426112i \(-0.859883\pi\)
−0.904670 + 0.426112i \(0.859883\pi\)
\(180\) −1.30867e20 −8.85142
\(181\) −7.12996e18 −0.460065 −0.230033 0.973183i \(-0.573883\pi\)
−0.230033 + 0.973183i \(0.573883\pi\)
\(182\) 2.62038e19 1.61346
\(183\) −1.27256e19 −0.747904
\(184\) 3.42598e19 1.92235
\(185\) −2.03381e18 −0.108981
\(186\) 1.07377e20 5.49603
\(187\) 1.21366e19 0.593529
\(188\) 3.23604e19 1.51242
\(189\) 3.97927e19 1.77778
\(190\) −1.82054e18 −0.0777669
\(191\) 7.07241e18 0.288924 0.144462 0.989510i \(-0.453855\pi\)
0.144462 + 0.989510i \(0.453855\pi\)
\(192\) −1.20122e20 −4.69420
\(193\) −3.38792e19 −1.26676 −0.633382 0.773840i \(-0.718334\pi\)
−0.633382 + 0.773840i \(0.718334\pi\)
\(194\) 3.46743e19 1.24077
\(195\) 1.01646e20 3.48173
\(196\) −4.93878e19 −1.61973
\(197\) 2.07684e19 0.652289 0.326144 0.945320i \(-0.394250\pi\)
0.326144 + 0.945320i \(0.394250\pi\)
\(198\) −1.89609e20 −5.70432
\(199\) −1.07855e19 −0.310878 −0.155439 0.987845i \(-0.549679\pi\)
−0.155439 + 0.987845i \(0.549679\pi\)
\(200\) −8.75818e19 −2.41913
\(201\) −1.66414e19 −0.440578
\(202\) 6.06233e19 1.53870
\(203\) −4.69159e18 −0.114184
\(204\) −1.05180e20 −2.45514
\(205\) 2.84509e19 0.637071
\(206\) 7.91639e18 0.170081
\(207\) −7.76583e19 −1.60118
\(208\) 2.21994e20 4.39341
\(209\) −1.90593e18 −0.0362130
\(210\) 1.61194e20 2.94094
\(211\) 4.11001e18 0.0720181 0.0360091 0.999351i \(-0.488535\pi\)
0.0360091 + 0.999351i \(0.488535\pi\)
\(212\) −1.72746e20 −2.90772
\(213\) 4.64265e19 0.750827
\(214\) −6.79018e19 −1.05527
\(215\) −9.38250e19 −1.40149
\(216\) 6.13322e20 8.80708
\(217\) −6.85497e19 −0.946450
\(218\) 1.49399e20 1.98367
\(219\) −2.76611e20 −3.53260
\(220\) −3.36251e20 −4.13115
\(221\) 5.85989e19 0.692715
\(222\) 2.55373e19 0.290519
\(223\) −1.23930e20 −1.35701 −0.678507 0.734594i \(-0.737372\pi\)
−0.678507 + 0.734594i \(0.737372\pi\)
\(224\) 1.74356e20 1.83793
\(225\) 1.98526e20 2.01496
\(226\) −4.56892e19 −0.446572
\(227\) 1.40492e20 1.32261 0.661304 0.750118i \(-0.270003\pi\)
0.661304 + 0.750118i \(0.270003\pi\)
\(228\) 1.65175e19 0.149795
\(229\) −3.71721e19 −0.324800 −0.162400 0.986725i \(-0.551923\pi\)
−0.162400 + 0.986725i \(0.551923\pi\)
\(230\) −1.90596e20 −1.60483
\(231\) 1.68755e20 1.36948
\(232\) −7.23111e19 −0.565662
\(233\) −5.78190e18 −0.0436059 −0.0218029 0.999762i \(-0.506941\pi\)
−0.0218029 + 0.999762i \(0.506941\pi\)
\(234\) −9.15486e20 −6.65759
\(235\) −1.10906e20 −0.777821
\(236\) 6.46902e20 4.37609
\(237\) −4.27402e20 −2.78918
\(238\) 9.29287e19 0.585121
\(239\) −1.40901e20 −0.856115 −0.428057 0.903752i \(-0.640802\pi\)
−0.428057 + 0.903752i \(0.640802\pi\)
\(240\) 1.36561e21 8.00813
\(241\) 1.92876e20 1.09177 0.545887 0.837859i \(-0.316193\pi\)
0.545887 + 0.837859i \(0.316193\pi\)
\(242\) −1.39766e20 −0.763783
\(243\) −4.85871e20 −2.56370
\(244\) 2.03258e20 1.03570
\(245\) 1.69263e20 0.833012
\(246\) −3.57241e20 −1.69829
\(247\) −9.20239e18 −0.0422646
\(248\) −1.05655e21 −4.68869
\(249\) 5.60507e20 2.40374
\(250\) −1.26296e20 −0.523480
\(251\) 4.84963e20 1.94304 0.971521 0.236952i \(-0.0761483\pi\)
0.971521 + 0.236952i \(0.0761483\pi\)
\(252\) −1.04904e21 −4.06337
\(253\) −1.99536e20 −0.747304
\(254\) −9.11080e19 −0.329966
\(255\) 3.60475e20 1.26265
\(256\) 2.43734e20 0.825802
\(257\) −2.70164e20 −0.885514 −0.442757 0.896642i \(-0.646000\pi\)
−0.442757 + 0.896642i \(0.646000\pi\)
\(258\) 1.17810e21 3.73608
\(259\) −1.63032e19 −0.0500292
\(260\) −1.62352e21 −4.82152
\(261\) 1.63911e20 0.471155
\(262\) 1.19005e21 3.31133
\(263\) 4.41737e20 1.18998 0.594991 0.803733i \(-0.297156\pi\)
0.594991 + 0.803733i \(0.297156\pi\)
\(264\) 2.60101e21 6.78436
\(265\) 5.92039e20 1.49541
\(266\) −1.45936e19 −0.0357000
\(267\) 7.03804e19 0.166765
\(268\) 2.65801e20 0.610114
\(269\) 1.90827e20 0.424371 0.212186 0.977229i \(-0.431942\pi\)
0.212186 + 0.977229i \(0.431942\pi\)
\(270\) −3.41208e21 −7.35236
\(271\) −9.03682e19 −0.188702 −0.0943510 0.995539i \(-0.530078\pi\)
−0.0943510 + 0.995539i \(0.530078\pi\)
\(272\) 7.87275e20 1.59328
\(273\) 8.14799e20 1.59834
\(274\) −1.50700e20 −0.286572
\(275\) 5.10095e20 0.940423
\(276\) 1.72925e21 3.09123
\(277\) −1.10542e20 −0.191623 −0.0958117 0.995399i \(-0.530545\pi\)
−0.0958117 + 0.995399i \(0.530545\pi\)
\(278\) −1.61351e21 −2.71263
\(279\) 2.39493e21 3.90533
\(280\) −1.58610e21 −2.50893
\(281\) −1.15804e21 −1.77713 −0.888567 0.458748i \(-0.848298\pi\)
−0.888567 + 0.458748i \(0.848298\pi\)
\(282\) 1.39258e21 2.07350
\(283\) 6.66784e20 0.963386 0.481693 0.876340i \(-0.340022\pi\)
0.481693 + 0.876340i \(0.340022\pi\)
\(284\) −7.41539e20 −1.03975
\(285\) −5.66092e19 −0.0770381
\(286\) −2.35226e21 −3.10724
\(287\) 2.28064e20 0.292456
\(288\) −6.09150e21 −7.58382
\(289\) −6.19426e20 −0.748786
\(290\) 4.02286e20 0.472228
\(291\) 1.07819e21 1.22915
\(292\) 4.41812e21 4.89196
\(293\) 7.96814e20 0.857003 0.428502 0.903541i \(-0.359042\pi\)
0.428502 + 0.903541i \(0.359042\pi\)
\(294\) −2.12534e21 −2.22063
\(295\) −2.21708e21 −2.25058
\(296\) −2.51279e20 −0.247843
\(297\) −3.57212e21 −3.42370
\(298\) −1.34342e21 −1.25133
\(299\) −9.63420e20 −0.872188
\(300\) −4.42066e21 −3.89007
\(301\) −7.52107e20 −0.643375
\(302\) −1.26659e21 −1.05336
\(303\) 1.88507e21 1.52428
\(304\) −1.23634e20 −0.0972104
\(305\) −6.96612e20 −0.532651
\(306\) −3.24667e21 −2.41438
\(307\) −1.18009e21 −0.853568 −0.426784 0.904354i \(-0.640354\pi\)
−0.426784 + 0.904354i \(0.640354\pi\)
\(308\) −2.69541e21 −1.89646
\(309\) 2.46158e20 0.168487
\(310\) 5.87788e21 3.91423
\(311\) 2.73278e21 1.77069 0.885343 0.464939i \(-0.153924\pi\)
0.885343 + 0.464939i \(0.153924\pi\)
\(312\) 1.25584e22 7.91811
\(313\) 2.00382e20 0.122951 0.0614755 0.998109i \(-0.480419\pi\)
0.0614755 + 0.998109i \(0.480419\pi\)
\(314\) 2.15789e20 0.128863
\(315\) 3.59529e21 2.08975
\(316\) 6.82661e21 3.86247
\(317\) 1.57164e21 0.865666 0.432833 0.901474i \(-0.357514\pi\)
0.432833 + 0.901474i \(0.357514\pi\)
\(318\) −7.43388e21 −3.98644
\(319\) 4.21155e20 0.219898
\(320\) −6.57557e21 −3.34317
\(321\) −2.11139e21 −1.04538
\(322\) −1.52783e21 −0.736718
\(323\) −3.26353e19 −0.0153273
\(324\) 1.65123e22 7.55395
\(325\) 2.46289e21 1.09758
\(326\) 1.94778e21 0.845650
\(327\) 4.64553e21 1.96508
\(328\) 3.51514e21 1.44882
\(329\) −8.89033e20 −0.357069
\(330\) −1.44701e22 −5.66374
\(331\) 3.70721e21 1.41419 0.707097 0.707117i \(-0.250004\pi\)
0.707097 + 0.707117i \(0.250004\pi\)
\(332\) −8.95260e21 −3.32870
\(333\) 5.69586e20 0.206435
\(334\) 6.09668e21 2.15401
\(335\) −9.10962e20 −0.313776
\(336\) 1.09468e22 3.67624
\(337\) −1.59611e21 −0.522648 −0.261324 0.965251i \(-0.584159\pi\)
−0.261324 + 0.965251i \(0.584159\pi\)
\(338\) −5.41157e21 −1.72795
\(339\) −1.42069e21 −0.442388
\(340\) −5.75763e21 −1.74853
\(341\) 6.15358e21 1.82270
\(342\) 5.09858e20 0.147308
\(343\) 3.53856e21 0.997303
\(344\) −1.15922e22 −3.18726
\(345\) −5.92655e21 −1.58979
\(346\) −6.64813e21 −1.74001
\(347\) 2.65739e21 0.678665 0.339333 0.940666i \(-0.389799\pi\)
0.339333 + 0.940666i \(0.389799\pi\)
\(348\) −3.64988e21 −0.909609
\(349\) −2.90036e21 −0.705401 −0.352701 0.935736i \(-0.614737\pi\)
−0.352701 + 0.935736i \(0.614737\pi\)
\(350\) 3.90576e21 0.927101
\(351\) −1.72472e22 −3.99585
\(352\) −1.56516e22 −3.53953
\(353\) 2.61779e21 0.577896 0.288948 0.957345i \(-0.406695\pi\)
0.288948 + 0.957345i \(0.406695\pi\)
\(354\) 2.78386e22 5.99956
\(355\) 2.54143e21 0.534733
\(356\) −1.12414e21 −0.230938
\(357\) 2.88959e21 0.579638
\(358\) 1.75367e22 3.43512
\(359\) 2.58164e21 0.493847 0.246924 0.969035i \(-0.420580\pi\)
0.246924 + 0.969035i \(0.420580\pi\)
\(360\) 5.54140e22 10.3526
\(361\) −5.47526e21 −0.999065
\(362\) 4.90076e21 0.873455
\(363\) −4.34597e21 −0.756625
\(364\) −1.30142e22 −2.21338
\(365\) −1.51419e22 −2.51589
\(366\) 8.74694e21 1.41993
\(367\) 8.30226e21 1.31685 0.658423 0.752648i \(-0.271224\pi\)
0.658423 + 0.752648i \(0.271224\pi\)
\(368\) −1.29435e22 −2.00607
\(369\) −7.96792e21 −1.20676
\(370\) 1.39793e21 0.206906
\(371\) 4.74582e21 0.686489
\(372\) −5.33291e22 −7.53962
\(373\) 9.06960e21 1.25332 0.626661 0.779292i \(-0.284421\pi\)
0.626661 + 0.779292i \(0.284421\pi\)
\(374\) −8.34204e21 −1.12684
\(375\) −3.92714e21 −0.518574
\(376\) −1.37026e22 −1.76891
\(377\) 2.03346e21 0.256646
\(378\) −2.73514e22 −3.37520
\(379\) 4.74499e21 0.572535 0.286267 0.958150i \(-0.407585\pi\)
0.286267 + 0.958150i \(0.407585\pi\)
\(380\) 9.04180e20 0.106683
\(381\) −2.83298e21 −0.326874
\(382\) −4.86120e21 −0.548536
\(383\) −1.67466e22 −1.84815 −0.924077 0.382207i \(-0.875164\pi\)
−0.924077 + 0.382207i \(0.875164\pi\)
\(384\) 3.04852e22 3.29059
\(385\) 9.23780e21 0.975331
\(386\) 2.32868e22 2.40501
\(387\) 2.62765e22 2.65475
\(388\) −1.72212e22 −1.70213
\(389\) −1.95067e22 −1.88631 −0.943153 0.332358i \(-0.892156\pi\)
−0.943153 + 0.332358i \(0.892156\pi\)
\(390\) −6.98660e22 −6.61023
\(391\) −3.41666e21 −0.316300
\(392\) 2.09127e22 1.89443
\(393\) 3.70042e22 3.28031
\(394\) −1.42751e22 −1.23840
\(395\) −2.33964e22 −1.98643
\(396\) 9.41701e22 7.82535
\(397\) 1.61283e20 0.0131180 0.00655902 0.999978i \(-0.497912\pi\)
0.00655902 + 0.999978i \(0.497912\pi\)
\(398\) 7.41341e21 0.590217
\(399\) −4.53783e20 −0.0353654
\(400\) 3.30889e22 2.52448
\(401\) −1.38546e22 −1.03483 −0.517413 0.855736i \(-0.673105\pi\)
−0.517413 + 0.855736i \(0.673105\pi\)
\(402\) 1.14384e22 0.836458
\(403\) 2.97113e22 2.12730
\(404\) −3.01089e22 −2.11083
\(405\) −5.65914e22 −3.88492
\(406\) 3.22475e21 0.216783
\(407\) 1.46350e21 0.0963477
\(408\) 4.45371e22 2.87151
\(409\) 8.57698e20 0.0541609 0.0270805 0.999633i \(-0.491379\pi\)
0.0270805 + 0.999633i \(0.491379\pi\)
\(410\) −1.95556e22 −1.20951
\(411\) −4.68598e21 −0.283886
\(412\) −3.93172e21 −0.233322
\(413\) −1.77723e22 −1.03316
\(414\) 5.33782e22 3.03991
\(415\) 3.06826e22 1.71192
\(416\) −7.55704e22 −4.13103
\(417\) −5.01717e22 −2.68721
\(418\) 1.31004e21 0.0687520
\(419\) 3.23264e22 1.66241 0.831205 0.555966i \(-0.187652\pi\)
0.831205 + 0.555966i \(0.187652\pi\)
\(420\) −8.00580e22 −4.03446
\(421\) −1.49065e21 −0.0736171 −0.0368086 0.999322i \(-0.511719\pi\)
−0.0368086 + 0.999322i \(0.511719\pi\)
\(422\) −2.82500e21 −0.136730
\(423\) 3.10603e22 1.47337
\(424\) 7.31470e22 3.40085
\(425\) 8.73435e21 0.398038
\(426\) −3.19112e22 −1.42548
\(427\) −5.58409e21 −0.244521
\(428\) 3.37238e22 1.44765
\(429\) −7.31430e22 −3.07812
\(430\) 6.44903e22 2.66080
\(431\) 2.87893e22 1.16459 0.582297 0.812976i \(-0.302154\pi\)
0.582297 + 0.812976i \(0.302154\pi\)
\(432\) −2.31716e23 −9.19062
\(433\) −5.12762e21 −0.199420 −0.0997099 0.995017i \(-0.531791\pi\)
−0.0997099 + 0.995017i \(0.531791\pi\)
\(434\) 4.71175e22 1.79688
\(435\) 1.25090e22 0.467803
\(436\) −7.41999e22 −2.72125
\(437\) 5.36554e20 0.0192984
\(438\) 1.90128e23 6.70680
\(439\) −9.40876e21 −0.325525 −0.162762 0.986665i \(-0.552040\pi\)
−0.162762 + 0.986665i \(0.552040\pi\)
\(440\) 1.42381e23 4.83176
\(441\) −4.74037e22 −1.57792
\(442\) −4.02778e22 −1.31515
\(443\) 4.10051e22 1.31343 0.656713 0.754140i \(-0.271946\pi\)
0.656713 + 0.754140i \(0.271946\pi\)
\(444\) −1.26832e22 −0.398543
\(445\) 3.85268e21 0.118769
\(446\) 8.51828e22 2.57635
\(447\) −4.17732e22 −1.23961
\(448\) −5.27102e22 −1.53473
\(449\) 1.16331e22 0.332355 0.166177 0.986096i \(-0.446858\pi\)
0.166177 + 0.986096i \(0.446858\pi\)
\(450\) −1.36456e23 −3.82549
\(451\) −2.04729e22 −0.563221
\(452\) 2.26918e22 0.612621
\(453\) −3.93843e22 −1.04349
\(454\) −9.65667e22 −2.51103
\(455\) 4.46028e22 1.13832
\(456\) −6.99413e21 −0.175199
\(457\) 4.03849e21 0.0992959 0.0496479 0.998767i \(-0.484190\pi\)
0.0496479 + 0.998767i \(0.484190\pi\)
\(458\) 2.55501e22 0.616647
\(459\) −6.11653e22 −1.44910
\(460\) 9.46607e22 2.20155
\(461\) 5.71596e21 0.130506 0.0652531 0.997869i \(-0.479215\pi\)
0.0652531 + 0.997869i \(0.479215\pi\)
\(462\) −1.15993e23 −2.60002
\(463\) −2.97167e22 −0.653977 −0.326988 0.945028i \(-0.606034\pi\)
−0.326988 + 0.945028i \(0.606034\pi\)
\(464\) 2.73195e22 0.590296
\(465\) 1.82771e23 3.87755
\(466\) 3.97417e21 0.0827879
\(467\) 9.82343e21 0.200942 0.100471 0.994940i \(-0.467965\pi\)
0.100471 + 0.994940i \(0.467965\pi\)
\(468\) 4.54681e23 9.13307
\(469\) −7.30233e21 −0.144043
\(470\) 7.62312e22 1.47673
\(471\) 6.70990e21 0.127655
\(472\) −2.73923e23 −5.11825
\(473\) 6.75153e22 1.23903
\(474\) 2.93774e23 5.29538
\(475\) −1.37165e21 −0.0242855
\(476\) −4.61535e22 −0.802686
\(477\) −1.65806e23 −2.83265
\(478\) 9.68480e22 1.62537
\(479\) −9.02271e22 −1.48760 −0.743798 0.668404i \(-0.766978\pi\)
−0.743798 + 0.668404i \(0.766978\pi\)
\(480\) −4.64877e23 −7.52987
\(481\) 7.06622e21 0.112449
\(482\) −1.32573e23 −2.07278
\(483\) −4.75076e22 −0.729814
\(484\) 6.94153e22 1.04778
\(485\) 5.90209e22 0.875388
\(486\) 3.33962e23 4.86731
\(487\) −5.49419e22 −0.786878 −0.393439 0.919351i \(-0.628715\pi\)
−0.393439 + 0.919351i \(0.628715\pi\)
\(488\) −8.60672e22 −1.21135
\(489\) 6.05657e22 0.837725
\(490\) −1.16343e23 −1.58151
\(491\) 1.84297e21 0.0246221 0.0123111 0.999924i \(-0.496081\pi\)
0.0123111 + 0.999924i \(0.496081\pi\)
\(492\) 1.77425e23 2.32977
\(493\) 7.21143e21 0.0930728
\(494\) 6.32524e21 0.0802413
\(495\) −3.22743e23 −4.02450
\(496\) 3.99171e23 4.89288
\(497\) 2.03722e22 0.245476
\(498\) −3.85263e23 −4.56360
\(499\) 1.42761e23 1.66247 0.831236 0.555919i \(-0.187634\pi\)
0.831236 + 0.555919i \(0.187634\pi\)
\(500\) 6.27256e22 0.718124
\(501\) 1.89575e23 2.13383
\(502\) −3.33338e23 −3.68896
\(503\) −3.50135e22 −0.380985 −0.190493 0.981689i \(-0.561009\pi\)
−0.190493 + 0.981689i \(0.561009\pi\)
\(504\) 4.44202e23 4.75249
\(505\) 1.03190e23 1.08558
\(506\) 1.37151e23 1.41879
\(507\) −1.68271e23 −1.71176
\(508\) 4.52492e22 0.452657
\(509\) 9.02728e22 0.888087 0.444044 0.896005i \(-0.353544\pi\)
0.444044 + 0.896005i \(0.353544\pi\)
\(510\) −2.47772e23 −2.39721
\(511\) −1.21378e23 −1.15495
\(512\) 1.94245e22 0.181784
\(513\) 9.60543e21 0.0884137
\(514\) 1.85696e23 1.68119
\(515\) 1.34749e22 0.119995
\(516\) −5.85111e23 −5.12526
\(517\) 7.98068e22 0.687655
\(518\) 1.12059e22 0.0949828
\(519\) −2.06722e23 −1.72371
\(520\) 6.87459e23 5.63921
\(521\) −5.91132e22 −0.477050 −0.238525 0.971136i \(-0.576664\pi\)
−0.238525 + 0.971136i \(0.576664\pi\)
\(522\) −1.12664e23 −0.894509
\(523\) 8.05353e22 0.629103 0.314552 0.949240i \(-0.398146\pi\)
0.314552 + 0.949240i \(0.398146\pi\)
\(524\) −5.91043e23 −4.54258
\(525\) 1.21449e23 0.918413
\(526\) −3.03627e23 −2.25924
\(527\) 1.05368e23 0.771467
\(528\) −9.82675e23 −7.07981
\(529\) −8.48770e22 −0.601751
\(530\) −4.06937e23 −2.83911
\(531\) 6.20913e23 4.26312
\(532\) 7.24797e21 0.0489742
\(533\) −9.88491e22 −0.657342
\(534\) −4.83758e22 −0.316612
\(535\) −1.15579e23 −0.744513
\(536\) −1.12550e23 −0.713586
\(537\) 5.45299e23 3.40293
\(538\) −1.31165e23 −0.805689
\(539\) −1.21800e23 −0.736447
\(540\) 1.69462e24 10.0862
\(541\) −8.96982e22 −0.525542 −0.262771 0.964858i \(-0.584636\pi\)
−0.262771 + 0.964858i \(0.584636\pi\)
\(542\) 6.21143e22 0.358260
\(543\) 1.52388e23 0.865271
\(544\) −2.68002e23 −1.49812
\(545\) 2.54300e23 1.39951
\(546\) −5.60050e23 −3.03452
\(547\) 1.79289e23 0.956450 0.478225 0.878237i \(-0.341280\pi\)
0.478225 + 0.878237i \(0.341280\pi\)
\(548\) 7.48459e22 0.393127
\(549\) 1.95092e23 1.00896
\(550\) −3.50613e23 −1.78544
\(551\) −1.13249e21 −0.00567864
\(552\) −7.32231e23 −3.61548
\(553\) −1.87547e23 −0.911897
\(554\) 7.59806e22 0.363806
\(555\) 4.34684e22 0.204967
\(556\) 8.01358e23 3.72127
\(557\) −3.64921e23 −1.66890 −0.834450 0.551084i \(-0.814214\pi\)
−0.834450 + 0.551084i \(0.814214\pi\)
\(558\) −1.64615e24 −7.41445
\(559\) 3.25983e23 1.44609
\(560\) 5.99238e23 2.61819
\(561\) −2.59393e23 −1.11628
\(562\) 7.95976e23 3.37397
\(563\) 2.04537e23 0.853987 0.426994 0.904255i \(-0.359573\pi\)
0.426994 + 0.904255i \(0.359573\pi\)
\(564\) −6.91634e23 −2.84449
\(565\) −7.77699e22 −0.315065
\(566\) −4.58312e23 −1.82903
\(567\) −4.53640e23 −1.78343
\(568\) 3.13996e23 1.21608
\(569\) −2.68877e21 −0.0102589 −0.00512943 0.999987i \(-0.501633\pi\)
−0.00512943 + 0.999987i \(0.501633\pi\)
\(570\) 3.89102e22 0.146261
\(571\) −2.01589e23 −0.746553 −0.373276 0.927720i \(-0.621766\pi\)
−0.373276 + 0.927720i \(0.621766\pi\)
\(572\) 1.16826e24 4.26260
\(573\) −1.51158e23 −0.543396
\(574\) −1.56759e23 −0.555242
\(575\) −1.43601e23 −0.501165
\(576\) 1.84155e24 6.33274
\(577\) 2.26835e23 0.768628 0.384314 0.923202i \(-0.374438\pi\)
0.384314 + 0.923202i \(0.374438\pi\)
\(578\) 4.25761e23 1.42161
\(579\) 7.24095e23 2.38247
\(580\) −1.99797e23 −0.647816
\(581\) 2.45954e23 0.785881
\(582\) −7.41089e23 −2.33359
\(583\) −4.26024e23 −1.32206
\(584\) −1.87080e24 −5.72160
\(585\) −1.55830e24 −4.69705
\(586\) −5.47688e23 −1.62706
\(587\) −5.40188e23 −1.58169 −0.790844 0.612017i \(-0.790358\pi\)
−0.790844 + 0.612017i \(0.790358\pi\)
\(588\) 1.05556e24 3.04632
\(589\) −1.65470e22 −0.0470694
\(590\) 1.52391e24 4.27283
\(591\) −4.43881e23 −1.22680
\(592\) 9.49346e22 0.258637
\(593\) 2.61741e23 0.702921 0.351460 0.936203i \(-0.385685\pi\)
0.351460 + 0.936203i \(0.385685\pi\)
\(594\) 2.45529e24 6.50006
\(595\) 1.58179e23 0.412813
\(596\) 6.67215e23 1.71661
\(597\) 2.30518e23 0.584687
\(598\) 6.62204e23 1.65589
\(599\) −3.31672e23 −0.817675 −0.408838 0.912607i \(-0.634066\pi\)
−0.408838 + 0.912607i \(0.634066\pi\)
\(600\) 1.87188e24 4.54979
\(601\) −4.68717e23 −1.12325 −0.561627 0.827391i \(-0.689824\pi\)
−0.561627 + 0.827391i \(0.689824\pi\)
\(602\) 5.16959e23 1.22148
\(603\) 2.55123e23 0.594364
\(604\) 6.29058e23 1.44503
\(605\) −2.37902e23 −0.538862
\(606\) −1.29570e24 −2.89392
\(607\) −1.64951e23 −0.363288 −0.181644 0.983364i \(-0.558142\pi\)
−0.181644 + 0.983364i \(0.558142\pi\)
\(608\) 4.20872e22 0.0914049
\(609\) 1.00273e23 0.214751
\(610\) 4.78815e23 1.01126
\(611\) 3.85331e23 0.802571
\(612\) 1.61247e24 3.31212
\(613\) 1.81599e22 0.0367874 0.0183937 0.999831i \(-0.494145\pi\)
0.0183937 + 0.999831i \(0.494145\pi\)
\(614\) 8.11131e23 1.62054
\(615\) −6.08077e23 −1.19818
\(616\) 1.14134e24 2.21809
\(617\) −4.73421e23 −0.907451 −0.453726 0.891141i \(-0.649905\pi\)
−0.453726 + 0.891141i \(0.649905\pi\)
\(618\) −1.69196e23 −0.319881
\(619\) 8.41475e22 0.156917 0.0784586 0.996917i \(-0.475000\pi\)
0.0784586 + 0.996917i \(0.475000\pi\)
\(620\) −2.91928e24 −5.36965
\(621\) 1.00561e24 1.82454
\(622\) −1.87837e24 −3.36173
\(623\) 3.08833e22 0.0545225
\(624\) −4.74464e24 −8.26294
\(625\) −6.77232e23 −1.16348
\(626\) −1.37732e23 −0.233428
\(627\) 4.07353e22 0.0681077
\(628\) −1.07173e23 −0.176777
\(629\) 2.50596e22 0.0407796
\(630\) −2.47121e24 −3.96749
\(631\) −5.94010e23 −0.940902 −0.470451 0.882426i \(-0.655909\pi\)
−0.470451 + 0.882426i \(0.655909\pi\)
\(632\) −2.89064e24 −4.51751
\(633\) −8.78427e22 −0.135449
\(634\) −1.08027e24 −1.64351
\(635\) −1.55080e23 −0.232797
\(636\) 3.69207e24 5.46871
\(637\) −5.88085e23 −0.859517
\(638\) −2.89480e23 −0.417487
\(639\) −7.11749e23 −1.01291
\(640\) 1.66878e24 2.34353
\(641\) 1.78206e23 0.246962 0.123481 0.992347i \(-0.460594\pi\)
0.123481 + 0.992347i \(0.460594\pi\)
\(642\) 1.45126e24 1.98471
\(643\) 1.09047e24 1.47171 0.735855 0.677139i \(-0.236780\pi\)
0.735855 + 0.677139i \(0.236780\pi\)
\(644\) 7.58806e23 1.01065
\(645\) 2.00531e24 2.63587
\(646\) 2.24318e22 0.0290996
\(647\) 4.67565e23 0.598626 0.299313 0.954155i \(-0.403243\pi\)
0.299313 + 0.954155i \(0.403243\pi\)
\(648\) −6.99192e24 −8.83505
\(649\) 1.59538e24 1.98969
\(650\) −1.69286e24 −2.08381
\(651\) 1.46511e24 1.78004
\(652\) −9.67375e23 −1.16009
\(653\) 1.75695e23 0.207969 0.103984 0.994579i \(-0.466841\pi\)
0.103984 + 0.994579i \(0.466841\pi\)
\(654\) −3.19309e24 −3.73079
\(655\) 2.02564e24 2.33621
\(656\) −1.32804e24 −1.51191
\(657\) 4.24062e24 4.76567
\(658\) 6.11075e23 0.677913
\(659\) −5.51681e22 −0.0604174 −0.0302087 0.999544i \(-0.509617\pi\)
−0.0302087 + 0.999544i \(0.509617\pi\)
\(660\) 7.18666e24 7.76969
\(661\) −1.41922e24 −1.51473 −0.757366 0.652990i \(-0.773514\pi\)
−0.757366 + 0.652990i \(0.773514\pi\)
\(662\) −2.54814e24 −2.68491
\(663\) −1.25243e24 −1.30283
\(664\) 3.79087e24 3.89323
\(665\) −2.48405e22 −0.0251870
\(666\) −3.91504e23 −0.391927
\(667\) −1.18563e23 −0.117187
\(668\) −3.02795e24 −2.95494
\(669\) 2.64874e24 2.55221
\(670\) 6.26148e23 0.595718
\(671\) 5.01273e23 0.470905
\(672\) −3.72649e24 −3.45669
\(673\) 1.56049e23 0.142933 0.0714667 0.997443i \(-0.477232\pi\)
0.0714667 + 0.997443i \(0.477232\pi\)
\(674\) 1.09708e24 0.992272
\(675\) −2.57076e24 −2.29604
\(676\) 2.68768e24 2.37045
\(677\) 1.81271e24 1.57879 0.789394 0.613887i \(-0.210395\pi\)
0.789394 + 0.613887i \(0.210395\pi\)
\(678\) 9.76510e23 0.839894
\(679\) 4.73115e23 0.401859
\(680\) 2.43800e24 2.04507
\(681\) −3.00271e24 −2.48750
\(682\) −4.22965e24 −3.46049
\(683\) −2.04896e22 −0.0165561 −0.00827805 0.999966i \(-0.502635\pi\)
−0.00827805 + 0.999966i \(0.502635\pi\)
\(684\) −2.53224e23 −0.202082
\(685\) −2.56514e23 −0.202181
\(686\) −2.43222e24 −1.89343
\(687\) 7.94475e23 0.610869
\(688\) 4.37958e24 3.32607
\(689\) −2.05697e24 −1.54299
\(690\) 4.07360e24 3.01829
\(691\) 1.33185e24 0.974746 0.487373 0.873194i \(-0.337955\pi\)
0.487373 + 0.873194i \(0.337955\pi\)
\(692\) 3.30183e24 2.38700
\(693\) −2.58713e24 −1.84750
\(694\) −1.82655e24 −1.28848
\(695\) −2.74644e24 −1.91381
\(696\) 1.54550e24 1.06387
\(697\) −3.50557e23 −0.238386
\(698\) 1.99356e24 1.33924
\(699\) 1.23576e23 0.0820121
\(700\) −1.93981e24 −1.27182
\(701\) −1.48023e24 −0.958796 −0.479398 0.877598i \(-0.659145\pi\)
−0.479398 + 0.877598i \(0.659145\pi\)
\(702\) 1.18548e25 7.58630
\(703\) −3.93537e21 −0.00248808
\(704\) 4.73170e24 2.95563
\(705\) 2.37039e24 1.46289
\(706\) −1.79933e24 −1.09716
\(707\) 8.27179e23 0.498350
\(708\) −1.38262e25 −8.23036
\(709\) −4.36708e23 −0.256861 −0.128431 0.991718i \(-0.540994\pi\)
−0.128431 + 0.991718i \(0.540994\pi\)
\(710\) −1.74684e24 −1.01521
\(711\) 6.55236e24 3.76275
\(712\) 4.76003e23 0.270103
\(713\) −1.73234e24 −0.971343
\(714\) −1.98616e24 −1.10047
\(715\) −4.00391e24 −2.19221
\(716\) −8.70968e24 −4.71239
\(717\) 3.01146e24 1.61014
\(718\) −1.77448e24 −0.937593
\(719\) 2.20556e24 1.15166 0.575830 0.817570i \(-0.304679\pi\)
0.575830 + 0.817570i \(0.304679\pi\)
\(720\) −2.09357e25 −10.8034
\(721\) 1.08016e23 0.0550855
\(722\) 3.76341e24 1.89677
\(723\) −4.12231e24 −2.05336
\(724\) −2.43399e24 −1.19823
\(725\) 3.03094e23 0.147470
\(726\) 2.98719e24 1.43649
\(727\) 2.71744e24 1.29157 0.645783 0.763521i \(-0.276531\pi\)
0.645783 + 0.763521i \(0.276531\pi\)
\(728\) 5.51072e24 2.58876
\(729\) 4.13796e24 1.92133
\(730\) 1.04077e25 4.77653
\(731\) 1.15606e24 0.524426
\(732\) −4.34421e24 −1.94790
\(733\) −1.99267e24 −0.883186 −0.441593 0.897216i \(-0.645586\pi\)
−0.441593 + 0.897216i \(0.645586\pi\)
\(734\) −5.70654e24 −2.50009
\(735\) −3.61765e24 −1.56669
\(736\) 4.40620e24 1.88627
\(737\) 6.55517e23 0.277402
\(738\) 5.47673e24 2.29109
\(739\) 4.76635e24 1.97110 0.985550 0.169385i \(-0.0541781\pi\)
0.985550 + 0.169385i \(0.0541781\pi\)
\(740\) −6.94291e23 −0.283839
\(741\) 1.96682e23 0.0794894
\(742\) −3.26203e24 −1.30333
\(743\) −1.39092e24 −0.549410 −0.274705 0.961529i \(-0.588580\pi\)
−0.274705 + 0.961529i \(0.588580\pi\)
\(744\) 2.25816e25 8.81828
\(745\) −2.28670e24 −0.882838
\(746\) −6.23396e24 −2.37949
\(747\) −8.59294e24 −3.24277
\(748\) 4.14311e24 1.54584
\(749\) −9.26490e23 −0.341779
\(750\) 2.69931e24 0.984538
\(751\) −4.08147e24 −1.47190 −0.735949 0.677037i \(-0.763264\pi\)
−0.735949 + 0.677037i \(0.763264\pi\)
\(752\) 5.17691e24 1.84595
\(753\) −1.03651e25 −3.65439
\(754\) −1.39769e24 −0.487254
\(755\) −2.15593e24 −0.743165
\(756\) 1.35842e25 4.63020
\(757\) 3.54143e24 1.19361 0.596806 0.802385i \(-0.296436\pi\)
0.596806 + 0.802385i \(0.296436\pi\)
\(758\) −3.26146e24 −1.08698
\(759\) 4.26467e24 1.40550
\(760\) −3.82864e23 −0.124775
\(761\) 4.24643e24 1.36853 0.684265 0.729234i \(-0.260123\pi\)
0.684265 + 0.729234i \(0.260123\pi\)
\(762\) 1.94724e24 0.620587
\(763\) 2.03849e24 0.642465
\(764\) 2.41434e24 0.752497
\(765\) −5.52632e24 −1.70339
\(766\) 1.15108e25 3.50881
\(767\) 7.70298e24 2.32219
\(768\) −5.20929e24 −1.55313
\(769\) −4.79103e24 −1.41272 −0.706358 0.707855i \(-0.749663\pi\)
−0.706358 + 0.707855i \(0.749663\pi\)
\(770\) −6.34958e24 −1.85171
\(771\) 5.77418e24 1.66544
\(772\) −1.15655e25 −3.29926
\(773\) −2.04679e24 −0.577493 −0.288747 0.957406i \(-0.593239\pi\)
−0.288747 + 0.957406i \(0.593239\pi\)
\(774\) −1.80611e25 −5.04018
\(775\) 4.42856e24 1.22236
\(776\) 7.29209e24 1.99080
\(777\) 3.48446e23 0.0940928
\(778\) 1.34079e25 3.58124
\(779\) 5.50517e22 0.0145446
\(780\) 3.46993e25 9.06810
\(781\) −1.82878e24 −0.472745
\(782\) 2.34843e24 0.600510
\(783\) −2.12252e24 −0.536879
\(784\) −7.90091e24 −1.97693
\(785\) 3.67305e23 0.0909149
\(786\) −2.54347e25 −6.22781
\(787\) −4.98402e24 −1.20724 −0.603621 0.797271i \(-0.706276\pi\)
−0.603621 + 0.797271i \(0.706276\pi\)
\(788\) 7.08980e24 1.69887
\(789\) −9.44120e24 −2.23807
\(790\) 1.60814e25 3.77133
\(791\) −6.23409e23 −0.144635
\(792\) −3.98752e25 −9.15248
\(793\) 2.42029e24 0.549599
\(794\) −1.10857e23 −0.0249052
\(795\) −1.26536e25 −2.81250
\(796\) −3.68191e24 −0.809677
\(797\) 7.29954e24 1.58818 0.794090 0.607800i \(-0.207948\pi\)
0.794090 + 0.607800i \(0.207948\pi\)
\(798\) 3.11907e23 0.0671429
\(799\) 1.36653e24 0.291053
\(800\) −1.12640e25 −2.37372
\(801\) −1.07898e24 −0.224976
\(802\) 9.52293e24 1.96467
\(803\) 1.08959e25 2.22424
\(804\) −5.68094e24 −1.14748
\(805\) −2.60060e24 −0.519768
\(806\) −2.04220e25 −4.03878
\(807\) −4.07853e24 −0.798139
\(808\) 1.27492e25 2.46881
\(809\) 2.51784e24 0.482464 0.241232 0.970467i \(-0.422448\pi\)
0.241232 + 0.970467i \(0.422448\pi\)
\(810\) 3.88979e25 7.37571
\(811\) 1.40479e24 0.263593 0.131796 0.991277i \(-0.457926\pi\)
0.131796 + 0.991277i \(0.457926\pi\)
\(812\) −1.60159e24 −0.297389
\(813\) 1.93143e24 0.354903
\(814\) −1.00594e24 −0.182921
\(815\) 3.31542e24 0.596621
\(816\) −1.68263e25 −2.99656
\(817\) −1.81549e23 −0.0319967
\(818\) −5.89536e23 −0.102827
\(819\) −1.24914e25 −2.15624
\(820\) 9.71241e24 1.65924
\(821\) 2.53580e24 0.428744 0.214372 0.976752i \(-0.431229\pi\)
0.214372 + 0.976752i \(0.431229\pi\)
\(822\) 3.22089e24 0.538972
\(823\) −3.15106e24 −0.521864 −0.260932 0.965357i \(-0.584030\pi\)
−0.260932 + 0.965357i \(0.584030\pi\)
\(824\) 1.66484e24 0.272892
\(825\) −1.09022e25 −1.76871
\(826\) 1.22157e25 1.96150
\(827\) 3.54565e24 0.563507 0.281754 0.959487i \(-0.409084\pi\)
0.281754 + 0.959487i \(0.409084\pi\)
\(828\) −2.65106e25 −4.17024
\(829\) −9.47300e24 −1.47494 −0.737470 0.675380i \(-0.763980\pi\)
−0.737470 + 0.675380i \(0.763980\pi\)
\(830\) −2.10896e25 −3.25016
\(831\) 2.36260e24 0.360397
\(832\) 2.28460e25 3.44955
\(833\) −2.08558e24 −0.311705
\(834\) 3.44854e25 5.10180
\(835\) 1.03775e25 1.51969
\(836\) −6.50637e23 −0.0943160
\(837\) −3.10125e25 −4.45011
\(838\) −2.22195e25 −3.15616
\(839\) −6.93284e24 −0.974843 −0.487421 0.873167i \(-0.662062\pi\)
−0.487421 + 0.873167i \(0.662062\pi\)
\(840\) 3.38996e25 4.71868
\(841\) 2.50246e23 0.0344828
\(842\) 1.02460e24 0.139766
\(843\) 2.47507e25 3.34235
\(844\) 1.40305e24 0.187570
\(845\) −9.21131e24 −1.21910
\(846\) −2.13492e25 −2.79727
\(847\) −1.90704e24 −0.247372
\(848\) −2.76353e25 −3.54895
\(849\) −1.42511e25 −1.81189
\(850\) −6.00354e24 −0.755695
\(851\) −4.12003e23 −0.0513451
\(852\) 1.58488e25 1.95551
\(853\) −2.16504e24 −0.264484 −0.132242 0.991217i \(-0.542218\pi\)
−0.132242 + 0.991217i \(0.542218\pi\)
\(854\) 3.83821e24 0.464234
\(855\) 8.67856e23 0.103929
\(856\) −1.42799e25 −1.69316
\(857\) 1.57593e25 1.85012 0.925058 0.379825i \(-0.124016\pi\)
0.925058 + 0.379825i \(0.124016\pi\)
\(858\) 5.02747e25 5.84396
\(859\) −6.13555e24 −0.706173 −0.353087 0.935591i \(-0.614868\pi\)
−0.353087 + 0.935591i \(0.614868\pi\)
\(860\) −3.20295e25 −3.65017
\(861\) −4.87439e24 −0.550039
\(862\) −1.97883e25 −2.21104
\(863\) 1.98669e24 0.219805 0.109903 0.993942i \(-0.464946\pi\)
0.109903 + 0.993942i \(0.464946\pi\)
\(864\) 7.88802e25 8.64174
\(865\) −1.13161e25 −1.22761
\(866\) 3.52445e24 0.378608
\(867\) 1.32389e25 1.40828
\(868\) −2.34011e25 −2.46501
\(869\) 1.68357e25 1.75616
\(870\) −8.59801e24 −0.888146
\(871\) 3.16503e24 0.323760
\(872\) 3.14191e25 3.18275
\(873\) −1.65293e25 −1.65819
\(874\) −3.68799e23 −0.0366389
\(875\) −1.72325e24 −0.169543
\(876\) −9.44279e25 −9.20058
\(877\) −1.30941e25 −1.26351 −0.631757 0.775166i \(-0.717666\pi\)
−0.631757 + 0.775166i \(0.717666\pi\)
\(878\) 6.46709e24 0.618024
\(879\) −1.70302e25 −1.61181
\(880\) −5.37925e25 −5.04218
\(881\) 1.13551e25 1.05414 0.527068 0.849823i \(-0.323291\pi\)
0.527068 + 0.849823i \(0.323291\pi\)
\(882\) 3.25828e25 2.99575
\(883\) 5.35270e24 0.487424 0.243712 0.969848i \(-0.421635\pi\)
0.243712 + 0.969848i \(0.421635\pi\)
\(884\) 2.00042e25 1.80416
\(885\) 4.73855e25 4.23280
\(886\) −2.81847e25 −2.49360
\(887\) 1.19457e25 1.04679 0.523397 0.852089i \(-0.324665\pi\)
0.523397 + 0.852089i \(0.324665\pi\)
\(888\) 5.37057e24 0.466133
\(889\) −1.24313e24 −0.106869
\(890\) −2.64813e24 −0.225488
\(891\) 4.07224e25 3.43458
\(892\) −4.23064e25 −3.53432
\(893\) −2.14601e23 −0.0177580
\(894\) 2.87127e25 2.35345
\(895\) 2.98501e25 2.42354
\(896\) 1.33771e25 1.07583
\(897\) 2.05911e25 1.64037
\(898\) −7.99599e24 −0.630991
\(899\) 3.65640e24 0.285822
\(900\) 6.77717e25 5.24791
\(901\) −7.29480e24 −0.559568
\(902\) 1.40720e25 1.06930
\(903\) 1.60747e25 1.21003
\(904\) −9.60856e24 −0.716517
\(905\) 8.34184e24 0.616239
\(906\) 2.70707e25 1.98111
\(907\) −1.15845e25 −0.839878 −0.419939 0.907552i \(-0.637949\pi\)
−0.419939 + 0.907552i \(0.637949\pi\)
\(908\) 4.79603e25 3.44471
\(909\) −2.88993e25 −2.05634
\(910\) −3.06576e25 −2.16116
\(911\) −1.97637e25 −1.38026 −0.690131 0.723685i \(-0.742447\pi\)
−0.690131 + 0.723685i \(0.742447\pi\)
\(912\) 2.64242e24 0.182829
\(913\) −2.20788e25 −1.51347
\(914\) −2.77585e24 −0.188518
\(915\) 1.48886e25 1.00179
\(916\) −1.26896e25 −0.845934
\(917\) 1.62377e25 1.07247
\(918\) 4.20418e25 2.75118
\(919\) 2.59306e25 1.68124 0.840621 0.541623i \(-0.182190\pi\)
0.840621 + 0.541623i \(0.182190\pi\)
\(920\) −4.00829e25 −2.57492
\(921\) 2.52219e25 1.60535
\(922\) −3.92885e24 −0.247772
\(923\) −8.82988e24 −0.551747
\(924\) 5.76087e25 3.56678
\(925\) 1.05324e24 0.0646137
\(926\) 2.04257e25 1.24161
\(927\) −3.77376e24 −0.227299
\(928\) −9.30003e24 −0.555043
\(929\) 2.52659e25 1.49418 0.747088 0.664725i \(-0.231451\pi\)
0.747088 + 0.664725i \(0.231451\pi\)
\(930\) −1.25627e26 −7.36171
\(931\) 3.27520e23 0.0190180
\(932\) −1.97379e24 −0.113571
\(933\) −5.84074e25 −3.33023
\(934\) −6.75211e24 −0.381497
\(935\) −1.41994e25 −0.795008
\(936\) −1.92529e26 −10.6820
\(937\) 2.92873e25 1.61025 0.805125 0.593106i \(-0.202098\pi\)
0.805125 + 0.593106i \(0.202098\pi\)
\(938\) 5.01924e24 0.273473
\(939\) −4.28274e24 −0.231241
\(940\) −3.78606e25 −2.02582
\(941\) 3.39276e25 1.79904 0.899521 0.436878i \(-0.143916\pi\)
0.899521 + 0.436878i \(0.143916\pi\)
\(942\) −4.61203e24 −0.242359
\(943\) 5.76348e24 0.300148
\(944\) 1.03489e26 5.34114
\(945\) −4.65563e25 −2.38126
\(946\) −4.64064e25 −2.35236
\(947\) −1.67626e25 −0.842104 −0.421052 0.907036i \(-0.638339\pi\)
−0.421052 + 0.907036i \(0.638339\pi\)
\(948\) −1.45904e26 −7.26436
\(949\) 5.26087e25 2.59594
\(950\) 9.42798e23 0.0461071
\(951\) −3.35906e25 −1.62811
\(952\) 1.95431e25 0.938816
\(953\) −2.11052e23 −0.0100485 −0.00502423 0.999987i \(-0.501599\pi\)
−0.00502423 + 0.999987i \(0.501599\pi\)
\(954\) 1.13966e26 5.37793
\(955\) −8.27450e24 −0.387002
\(956\) −4.81000e25 −2.22974
\(957\) −9.00130e24 −0.413575
\(958\) 6.20174e25 2.82427
\(959\) −2.05623e24 −0.0928142
\(960\) 1.40539e26 6.28769
\(961\) 3.08743e25 1.36914
\(962\) −4.85695e24 −0.213489
\(963\) 3.23689e25 1.41028
\(964\) 6.58429e25 2.84351
\(965\) 3.96376e25 1.69678
\(966\) 3.26542e25 1.38559
\(967\) 2.06300e25 0.867708 0.433854 0.900983i \(-0.357153\pi\)
0.433854 + 0.900983i \(0.357153\pi\)
\(968\) −2.93931e25 −1.22547
\(969\) 6.97510e23 0.0288269
\(970\) −4.05678e25 −1.66197
\(971\) 4.56860e25 1.85532 0.927662 0.373421i \(-0.121815\pi\)
0.927662 + 0.373421i \(0.121815\pi\)
\(972\) −1.65864e26 −6.67711
\(973\) −2.20156e25 −0.878562
\(974\) 3.77642e25 1.49392
\(975\) −5.26390e25 −2.06428
\(976\) 3.25166e25 1.26410
\(977\) −2.48939e25 −0.959379 −0.479689 0.877438i \(-0.659251\pi\)
−0.479689 + 0.877438i \(0.659251\pi\)
\(978\) −4.16297e25 −1.59046
\(979\) −2.77234e24 −0.105001
\(980\) 5.77822e25 2.16956
\(981\) −7.12190e25 −2.65100
\(982\) −1.26676e24 −0.0467463
\(983\) −3.55038e25 −1.29888 −0.649442 0.760411i \(-0.724998\pi\)
−0.649442 + 0.760411i \(0.724998\pi\)
\(984\) −7.51286e25 −2.72488
\(985\) −2.42984e25 −0.873714
\(986\) −4.95676e24 −0.176703
\(987\) 1.90012e25 0.671561
\(988\) −3.14146e24 −0.110077
\(989\) −1.90067e25 −0.660297
\(990\) 2.21836e26 7.64071
\(991\) −1.10853e25 −0.378549 −0.189275 0.981924i \(-0.560614\pi\)
−0.189275 + 0.981924i \(0.560614\pi\)
\(992\) −1.35885e26 −4.60067
\(993\) −7.92337e25 −2.65975
\(994\) −1.40028e25 −0.466048
\(995\) 1.26187e25 0.416409
\(996\) 1.91343e26 6.26048
\(997\) 2.84170e25 0.921870 0.460935 0.887434i \(-0.347514\pi\)
0.460935 + 0.887434i \(0.347514\pi\)
\(998\) −9.81263e25 −3.15628
\(999\) −7.37571e24 −0.235232
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 29.18.a.b.1.2 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.18.a.b.1.2 21 1.1 even 1 trivial